Question

Find the value of each of the following:
 $ ({3^0} + {4^{ - 1}}) \times {2^2} $

Answer 1

Hint: Simplify the given expression using the step by step approach. Anything raised to zero is one, also convert the inverse functions and then LCM (least common factor) and then multiply its value with the square of the number. Simplify for the resultant required value.

Complete step-by-step answer:
Take the given expression: $ ({3^0} + {4^{ - 1}}) \times {2^2} $
Place $ {3^0} = 1 $ in the above expression since anything raised to zero is one. Also place $ {4^{ - 1}} = \dfrac{1}{4} $ in the above expression.
 $ = (1 + \dfrac{1}{4}) \times {2^2} $
Find the LCM (least common multiple) for the above expression. LCM can be well defined as the least or the smallest number with which the given numbers are exactly divisible. LCM is also called the least common divisor.
 $ = (\dfrac{{4 + 1}}{4}) \times 4 $
Simplify the above expression finding the sum of the terms.
 $ = (\dfrac{5}{4}) \times 4 $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator of the above expression.
 $ = 5 $
Hence, the required solution is $ ({3^0} + {4^{ - 1}}) \times {2^2} = 5 $
So, the correct answer is “5”.

Note: Always remember the basic concepts that anything to the power zero is equal to one. Be clear with the concepts of squares and square-root and apply it accordingly. Square is the number which is multiplied with itself. Square of the number is always positive.